A Model-Based Design to Implement Controllers for Quadrotor Unmanned Aerial Vehicles

HIEN N.V., DIEM P.G.

Department of Aeronautical and Space Engineering, School of Transportation Engineering Hanoi University of Science and Technology

No1, Dai Co Viet, Hai Ba Trung, Hanoi VIETNAM

[hien.ngovan, diem.phamgia]@hust.edu.vn http://www.hust.edu.vn Abstract: - This paper presents a model-driven control design, which is based on the specialization of Model-Based Systems Engineering (MBSE) approach combined with the real-time UML/MARTE, hybrid automata and the Extended Kalman Filter (EKF) algorithm in order to conveniently implement and deploy controllers for quadrotor Unmanned Aerial Vehicles (UAVs). This model also creates a real-time communication pattern, which can permit the designed control components of a developed quadrotor UAV to be customized and reused in new control applications of various UAV typed Vertical Take Off and Landing (VTOL). To achieve this goal, the study is stepwise carried out as follows: the physical and dynamic model together with control structure of a quadrotor UAV are firstly adapted for developing entirely a quadrotor UAV controller. The use-case model combined with the realization hypotheses of hybrid automata and the EKF algorithm are then specialized to gather the requirement analysis of control. The specializations of real-time UML/MARTE’s features such as the ‘capsules, ports and protocols’ notation combined with the timing concurrency of evolution are next realized to precisely design structures and behaviors for the controller. The detailed design model is then converted into the implementation model by using object-oriented and open-source platforms in order to quickly simulate and realize this controller. Finally, a trajectory-tracking controller is developed and tested that permits an autonomous quadrotor UAV to reach and follow a reference trajectory in the Cartesian space with good reliability. Key-Words: - UAV control; autonomous flying robot; model-based control design; systems engineering; hybrid automata; EKF; real-time UML/MARTE; MBSE. Nomenclature CLF Control Lyapunov Functions MDE Model-Driven Engineering DoF Degrees of Freedom OMG Object Management Group EKF Extended Kalman Filters OO Object-Oriented GPS Global Positioning System OOA Object-Oriented Analysis HA Hybrid Automata OOD Object-Oriented Design HDS Hybrid Dynamic Systems OOImpl Object-Oriented Implementation IB Integral Backstepping PID Proportional-Integral-Derivative IDE Implementation Development Environment SMC Sliding-Mode Control IGCB Instantaneous Global Continuous Behavior SysML System Modeling Language IMU Inertial Measurement Unit UAV Unmanned Aerial Vehicles LQ Linear Quadratic UML Unified Modeling Language LOS Line-Of-Sight VTOL Vertical Take Off and Landing MARTE Modeling and Analysis of Real-Time and

Embedded Systems WP Way-Point

MBSE Model-Based Systems Engineering 1 Introduction Unmanned Aerial Vehicles (UAVs) have seen unprecedented levels of growth over the last decade, especially the quadrotor UAV. Even though UAVs have been mainly used for military applications,

there is a considerable and increasing interest for civilian applications. It is postulated that UAVs will be used extensively in the future for environmental monitoring, traffic monitoring, mapping, surveillance, etc. The quadrotor UAV is one of the

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miniature UAV types of which operating modes are capable of Vertical Take Off and Landing (VTOL), hovering and horizontal flight; so they can be more easily handled in turbulences such as wind and are easier to design and realize by using a compact airframe [1-3]. The problem of designing autonomous flight controllers for quadrotor UAVs is equally challenging because these controllers are closely connected with the dynamic models. Therefore, these control systems must take account of models with discrete events and continuous behaviors that can be called Hybrid Dynamic Systems (HDS) described in [4-6]. These behaviors are distributed on different operating modes, which are associated with processes related to the interactivity with users such as the designer, supervisor, maintainer etc. Furthermore, controlled systems do not always have the same behavior because they are associated with validity hypotheses to check at any moment; the security requirement forces to envisage events, and behaviors different from nominal behaviors. The behaviors of such systems are thus complex; in this paper, the quadrotor UAV controllers are considered as HDS of which behaviors can be modeled by Hybrid Automata (HA) [7-9]. In addition, the immersion in an industrial control context makes that designers and programmers must take into account costs and existing standards in order to effectively design and deploy the developed systems with reasonable cost. The customization and reusability are also factors to be associated with the production of new applications in order to reduce their costs, resources and time development. According to the Object Management Group (OMG) [10], UML appeared to us to be essential for its visual object-oriented design support, which has been largely spread and appreciated in the software industry. Furthermore, the System Modeling Language (SysML) [11], which is a UML profile for systems engineering, has been standardized by OMG. SysML supports the specification, analysis, design, verification and validation of a broad range of complex systems. However, both UML and SysML lack the constructs for modeling time and duration constraints of the developed system. Thus, the real-time UML/MARTE version [12-14] is chosen to model in detail the analysis and design artifacts for real-time and embedded control systems, e.g. the quadrotor UAV controller. This version also includes the ‘capsules, ports, protocols, connectors’ concepts that can be adapted by specializing a set of control capsules in precise behaviors and structures of the quadrotor UAV controller.

The paper aims to implement a control model integrating the quadrotor UAV dynamics into MDA combined with the real-time object paradigms and the specialization of HA features, which can permit us to conveniently realize and deploy the quadrotor UAV controller, and also allow the designed and implemented control elements to be closely customizable and re-usable in the realization of new applications for various UAV types of which operating modes are capable of VTOL. In our current model, the quadrotor dynamics and control architecture are also adapted for the control that are then combined with the models as follows: The Object-Oriented (OO) Analysis (OOA), OO Design (OOD) and OO Implementation (OOImpl) models; this control system permits a quadrotor UAV to track a reference trajectory in the Cartesian space. Here, the OOA includes the use-case model specialized closely with an implementable function block diagram, the EKF algorithm, HA and its evolution hypotheses of realization to precisely capture the requirement analysis for a quadrotor UAV controller; the OOD model is built on the identified OOA model by specifying the real-time UML/MARTE to entirely design the real-time control capsules with their timing concurrency of evolutions in detail. The detailed OOD elements is then converted into OOImpl models by using open-source platforms such as OpenModelica [15] and Arduino [16] in order to quickly simulate, realize and deploy the quadrotor UAV controller. Finally, a trajectory-tracking controller of an application of autonomous quadrotor UAV was completely deployed and tested. The paper is structured as follows: The second section brings the related works that have inspired us to define a model-based design for quadrotor UAV controllers. The quadrotor UAV dynamic model and control architecture are introduced in the third section. The fourth section presents the details of model-driven development to intensively realize quadrotor UAV controllers, including the OOA, OOD and OOImpl components. Following this described model, in the fifth section, it is applied to a case study. Conclusions and future works are reported in the final section. 2 Related work The autonomy architecture of general UAV basically consists of three main sub-systems as follows: the guidance sub-system, navigation sub-system and control system. All three of these sub-systems have their own individual tasks to complete, yet must also work cooperatively in order to reliably

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allow a UAV to complete its objectives. In present design and construction of quadrotor UAV controllers, there were many applications that have used the basic control methods combined with soft computing approaches [17-22] to make them more effective for control systems. For example, a model-based adaptive controller for quadrotor UAV with different payload has introduced by Tsay [23]; it is a gain stabilized control technique in which the large gain is used for large tracking error to get fast response, the small gain is used between large and small tracking error for good performance. The large gain is also used for small tracking error to cope with disturbance in this developed model. A Binary Observers (BO)-based linear feedback Sliding Mode Control (SMC) for quadrotor’s robust flight has been presented by Zhang, Zhou, Li, et al. [24]; in this study, the quadrotor has been divided into two subsystems, i.e. the rotational subsystem sensitive to unknown disturbances and the translational one subjected to both disturbances and measurement delay. The disturbance observer and delayed output observer were then designed with their interactions being considered, and disturbance observer based controller and BO-based controller were hierarchically proposed for attitude and position control respectively. The disturbances and real outputs were converged exponentially by observers’ estimations, which were compensated in the feedback control loop. A robust controller has been proposed by Liu, Li, Zuo, et al. [25] to address the attitude control problem for quadrotors with uncertainty in the input delays; their designed controller included a nominal controller to achieve desired tracking for the nominal system and a robust compensator to achieve the robust stability of the uncertain system with input delays. In particular, the different controllers based on Lyapunov theory, PID, Linear Quadratic (LQ), Backstepping and SMC techniques were implemented to the control design of a miniature quadrotor UAV, and were compared for attitude control that could be found in [26]. However, the above guidance and control models were based on the structural implementations. Thus, the designed control elements could be difficult to customize and reuse for realizing controllers of different UAV types of which operating modes are capable of VTOL, and for deploying appropriately into various software and hardware platforms. To achieve this goal, the Model-Based Systems Engineering (MBSE) approach can be specialized in order to intensively performing the whole of development lifecycle for quadrotor UAV controllers. The MBSE is the formalized application of modeling to support system requirements, design,

analysis, verification, and validation activities beginning in the conceptual design phase and continuing throughout development and later life cycle phases [27]. MBSE is intended to facilitate systems engineering activities that have traditionally been performed using the document-based approach and result in the enhanced specification and design quality, reuse of system specification and design artefacts, and communications among the development team. Following the MBSE approach, Barbieri, Fantuzzi and Borsari [28] have introduced a model-based design methodology, which supports the integrated development of complex mechatronic devices and the problem of devices interchangeability; this method was based on the W model [29] and on the SysML identification: the generation of a system model constantly refined and updated, during the design process, and whose information can be exported to or imported from domain specific models. A practical approach to the application of advanced software engineering methodologies for the design and realization of automatic machineries for smart manufacturing processes have been presented in [30]; the patterns presented in this work have driven control software programmers in the development stage of real-world systems, in order to cope with the increasing system complexity, preserving efficiency and reusability of mechatronic components. Herrera, Posadas, Peñil, et al. [31] have introduced the COMPLEX UML/MARTE methodology for Design Space Exploration of embedded systems, which was based on a novel combination of Model-Driven Engineering (MDE), Electronic System Level and design exploration technologies; this framework could enable capturing the set of possible design solutions, that is, the design space, in an abstract, standard and graphical way by relying on UML and the standard MARTE profile. In particular, the statistical findings from a complete survey about the use of real-time UML/MARTE and model-driven approaches for the design of real-time embedded systems can be seen in [32, 33]. In this section, we illustrated the structural implementations for quadrotor UAV controllers and the model-driven methodologies for real-time and embedded systems that could be used to make up a model-driven implementation to conveniently develop the quadrotor UAV controller. 3 Quadrotor UAV dynamics and control structure

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3.1 Overview of quadrotor UAV dynamics for control From the large field of guidance, navigation and

control of aerial vehicles in [18, 26, 34-39], the six DoF dynamic model of a quadrotor UAV in body coordinate frame can be written in equation systems (1).

⎩⎪⎪⎪⎨

⎪⎪⎪⎧ mx = (sinψsinϕ+ cosψsinθcosϕ)∑ Ti

4i=1 −∑ Hxi

4i=1 − 1

2CxAcρx|x|

my = (−cosψcosϕ+ sinψsinθcosϕ)∑ Ti4i=1 − ∑ Hyi

4i=1 − 1

2Cy Acρy|y|

mz = mg − (cosψcosϕ)∑ Ti4i=1

Ixx ϕ = θψIyy − Izz + Jr θΩr + l(−T2 + T4) − h∑ Hyi4i=1 + (−1)i+1 ∑ Rmxi

4i=1

Iyy θ = ϕψ(Izz − Ixx )− JrϕΩr + l(T1 − T3) − h∑ Hxi4i=1 + (−1)i+1 ∑ Rmyi

4i=1

Izz ψ = θϕIxx − Iyy + JrΩr + (−1)i ∑ Qi4i=1 + l(Hx2 − Hx4) + l(Hy3 − Hy1)

(1)

Where: Ixx, Iyy and Izz are inertia moments; φ, θ, ψ are respectively Roll, Pitch, Yaw (RPY) angles; Jr presents the rotor inertia; H is a set of hub forces; Rm is a set of rolling moments; Ti presents the thrust force (i = 1,4); Ωr is the overall residual propeller angular speed; Ac is fuselage area; C is the propulsion group cost factor; ρ is the air density; Qi presents the drag moment; h and l are respectively vertical distance and horizontal distance: propeller center to Center Of Gravity (CoG); x, y and z define the position in body coordinate frame. To develop controllers of quadrotor UAVs, it is advisable to simplify the model in order to comply with the real-time constraints of the embedded control loop. In our case study, we proposed that hub forces and rolling moments are neglected and thrust and drag coefficients are supposed constant. The system can be rewritten in state-space form 𝐱 =𝐟𝐟(𝐱𝐱,𝐮𝐮) with u inputs vector and x state vector.

𝐮𝐮 = [u1, u2, u3, u4]T (2) Here, ui is the control input (i = 1,4) and described by a set of equations (3); b and d are respectively the thrust and drag factors.

⎩⎪⎨

⎪⎧u1 = b(ω1

2 +ω22 + ω3

2 + ω42)

u2 = b(−ω22 +ω4

2) u3 = b(−ω1

2 +ω32)

u4 = d(−ω12 + ω2

2 −ω32 + ω4

2)

(3)

𝐱𝐱 is a 12-dimensional state vector for describing the motion of quadrotor UAV that is written as follows:

𝐱𝐱 = x, y, z, φ,θ,ψ, x, y, z, ϕ, θ, ψT

(4) A discrete state-space representation is required for modeling the quadrotor UAV controller in order to use a recursive estimation filter of motion states, e.g. the EKF; the developed system can be then described by a set of equations (5).

𝐱𝐱𝐤𝐤 = 𝐟𝐟𝐤𝐤−𝟏𝟏(𝐱𝐱𝐤𝐤−𝟏𝟏,𝐮𝐮𝐤𝐤−𝟏𝟏) + 𝐰𝐰𝐤𝐤−𝟏𝟏𝐲𝐲𝐤𝐤 = 𝐡𝐡𝐤𝐤(𝐱𝐱𝐤𝐤) + 𝐯𝐯𝐤𝐤

(5)

Where: xk is the vector of state variables at the kth instant of x; uk and yk are respectively the inputs and outputs of the system; wk and vk are the additive process and measurement noise; the first equation in

(5) is called the system’s evolution equation, while the second one is called the measurement equation. 3.2 Using control structure and technique Within the autonomy architecture of quadrotor UAVs are three main systems. These are the guidance system, which is responsible for generating the trajectory for the vehicle to follow; the navigation system, which produces an estimation of the current state of the vehicle; and the control system, which calculates and applies the appropriate forces to manoeuvre the vehicle. Fig. 1 shows out a functional block diagram, which captures how these sub-systems interact.

Fig. 1. Block diagram of guidance, navigation and control for quadrotor UAVs.

Here, the guidance system is responsible for producing the desired trajectory for the vehicle to follow. This task can be completed by implementing a common guidance approach based on the generations of way-points that take the desired way-points defined pre-mission and, with the possible inclusion of external environmental disturbances, generates a path for the quadrotor UAV to follow in order to reach each successive way-point. An alternative approach is based on Line-Of-Sight (LOS) guidance [40-42]; in this case, the heading control is computed by considering as input the angle formed by the vector from the quadrotor UAV to the next way-point rather than requiring the

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quadrotor UAV to exactly follow the line segment between the current and the following way-point. The navigation system addresses the task of determining the current state of the quadrotor UAV; for airborne vehicles, Global Positioning System (GPS) is readily available and is often used to provide continuous accurate positioning information to the navigation system. Overall, the task of the navigation system block is to provide the best estimate of the current state of the quadrotor UAV, regardless of what sensor information is available. The controllers are responsible for providing the corrective signals and events to enable the quadrotor UAV to follow the desired trajectory. This is achieved by receiving the desired state of the quadrotor UAV from the guidance system, and its current state combining the altitude, position, attitude and velocity from the navigation system. It then calculates and applies correcting forces and moments, through use of the various actuators on the quadrotor UAV, to minimize the difference between desired and current states. This allows the quadrotor UAV to track a desired trajectory even in the presence of unknown disturbances. Overall, the controllers of any quadrotor UAV composes of a sub-block of control law and a sub-block of control allocation. The first is responsible for generating the generalized forces and moments in six DoF based on current and desired states, while the second is responsible for distributing this generalized forces and moments amongst the actuators of quadrotor UAV in order to realize the navigation task allocation. From the above described quadrotor UAV dynamic model and general control structure together with characteristics of HDS in [4, 5, 43], we find that controllers of quadrotor UAVs are HDS whose dynamic behaviors can be modeled by HA. These control systems have the continuous/discrete parts and their interactions such as the motional components, e.g. horizontal transferring, VTOL, rotation, roll, pitch and yaw, and external interacting events from the guidance and navigation system, and environmental disturbances. In our model, we are interested in developing the trajectory-tracking controller of quadrotor UAVs, so we can use this hybrid dynamic model to find out the control algorithms with a specific guidance law such as the Line-Of-Sight (LOS) guidance implemented in [40, 41, 44]. Furthermore, Bouabdallah [26] has made the theoretical simulation and experiment evaluations for a quadrotor UAV controller with several control techniques using different approaches such as: Lyapunov theory, Proportional Integral Derivative

(PID) control, optimal control theory, Backstepping and SMC; it clearly brought out that the way is to follow a combination between PID and Backstepping into the so-called Integral Backstepping (IB) [45]. The goal of this approach was to bring together the robustness against disturbances offered by Backstepping and robustness against model uncertainties offered by the integral action. The stability analysis is performed by using Lyapunov theory; it means that IB is a recursive design technique using Control Lyapunov Functions (CLF). The CLF concept is a generalization of Lyapunov design results by, for instance, [46-48]. Hence, this can permit us to design the control law of quadrotor UAV controllers combined with the IB technique, the specialization of HA features and CLF for more complex flight maneuvers than a simple hovering. 4 Model-driven development for a quadrotor UAV controller As the previously stated, the real-time UML/MARTE version was chosen to model in detail the analysis and design artifacts for real-time and embedded control systems, e.g. the quadrotor UAV controller. Starting from the above adapted quadrotor UAV dynamics and control structures and real-time UML/MARTE features, we develop in detail a model-driven implementation for the quadrotor UAV controller, which includes three models as follows: OOA, OOD and OOImpl model so separate the specification of the operation of the system from the details of the way that system uses the capabilities of its platform. There are also transformation rules, which allow the OOD model be converted into various OOImpl models. i) In OOA model, the use case model in object collaboration is specialized by the implemented functional block diagram, HA and its realization hypotheses to closely capture the requirements analysis for a quadrotor UAV controller. ii) OOD model is built up by specifying the real-time control capsules, ports, protocols and their timing concurrency of evolutions together with the realization hypotheses of HA in order to model the precise behaviors and structures of quadrotor UAV controller. iii) OOD model is then converted into OOImpl model as follows: Object-Oriented simulation models are carried out in the OOImpl model in order to simulate the defined design model into the specific software platforms that permits us to theoretically evaluate the control performance and

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functionalities, and to easily identify control design elements of this system before we decide to realize and deploy it. The OO realization models are also performed in the OOImpl model in order to carry out its implementation phase with specific platforms, which can support object-oriented programming languages such as C++, Java, Ada, etc., and upload the implemented control program to compatible microcontrollers to completely deploy the quadrotor UAV controller. 4.1 OOA model for a quadrotor UAV controller From the above dynamic model (1), general control structure (Fig. 1) of quadrotor UAVs together with LOS guidance [41], we have developed the main use case model of controllers as shown in Fig. 2 combined with an example of trajectory-tracking scenarios and local state machine of the “Track a desired trajectory” use case which are respectively shown in Fig. 3a and Fig. 3b. Here, MDS is the Measurement and Display System combined with the guidance and navigation system; AES is the Air Environment System including disturbances generated by the weather. Here, it is necessary to provide industrial control constraints, e.g. the maximum tilted angle, velocity, altitude and other safe flying modes of the developed quadrotor UAV in order to ensure the operational safety of this system.

Fig. 2. Main use case model for a quadrotor UAV controller.

Actually, the real-time UML/MARTE version lacks the constructs for modeling internal continuous behaviors for each state on the state machine diagram, an implemented functional block diagram must be then defined in order to model continuous behaviors of the quadrotor UAV controller with events issued from outside. Starting from the considered dynamic model of quadrotor UAV, the

general architecture and the identified use case model with LOS guidance, we propose an implemented functional diagram for the quadrotor UAV controller as shown in Fig. 4.

Fig. 3. An example of trajectory-tracking scenarios

(a) and the local state machine of the “Track a desired trajectory” use case (b) for a quadrotor

UAV controller. Here, Desired trajectory and Take-off/Landing actions respectively give the desired position (xd, yd) altitude (zd) to the position and altitude controller; ΣTd is the desired overall thrust; the position controller receives the quadrotor UAV’s position (x, y) and desired thrust, it outputs desired roll (φd) and pitch (θd) while desired yaw (Ψd) comes directly from the guidance system; the attitude controller gives then the desired motor speeds (ωd1, ωd2, ωd3, ωd4) to the motor controllers; τφ,θ,Ψ and ΣT are respectively the overall torque and thrust acting on the quadrotor UAV. In our current model, the IB technique combined with the EKF algorithm are used for altitude, position, attitude and velocity control. The IB expansions combined with CLF for quadrotor UAV controllers were well known by

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many quadrotor UAV control applications, for instance, [26, 46, 49-51]. The state-space models (2), (4) and (5) are used for the estimation and prediction of the altitude, position, attitude and velocity corresponding to the sensors installed on the quadrotor UAV that are implemented in the Navigation System block. The standard navigation filter is based on EKF that composes of the predict/update scheme shown in Algorithm 1 for estimating the altitude, position, attitude and velocity of the quadrotor UAV. In Algorithm 1, . denotes an estimate; P is the state covariance; Q and R are respectively the covariance matrices of process and measurement noise, assumed as zero mean stationary white noises with zero cross-correlation; the state is recursively estimated starting from the assumed initial conditions as follows: 𝐱𝐱0|0 = 𝐱𝐱0 and 𝑃𝑃0|0 = 𝟎𝟎12×12. When the EKF does not use directly the measures of the accelerometer, as it was deemed too noisy for the position estimation; in the case in which data from one or

more sensors are not available for a period, the algorithm then uses the last available measure, but it gives a high value to the corresponding coefficient; the measure will be thus characterized by a low weight in the estimation process.

Fig. 4. An implemented functional block diagram for the quadrotor UAV controller.

Algorithm 1. Standard navigation filter based on EKF for a quadrotor UAV controller.

Function EKF algorithm Step EKF predict Data : 𝐱𝐱𝑘𝑘−1|𝑘𝑘−1,𝑃𝑃𝑘𝑘−1|𝑘𝑘−1, 𝐟𝐟𝑘𝑘−1(. ) Result : 𝐱𝐱𝑘𝑘|𝑘𝑘−1,𝑃𝑃𝑘𝑘 |𝑘𝑘−1

𝐹𝐹𝑘𝑘−1 = 𝜕𝜕𝐟𝐟𝑘𝑘−1𝜕𝜕𝐱𝐱

𝐱𝐱𝑘𝑘−1|𝑘𝑘−1𝐮𝐮𝑘𝑘−1

;

𝐱𝐱𝑘𝑘|𝑘𝑘−1 = 𝐟𝐟𝑘𝑘−1𝐱𝐱𝑘𝑘−1|𝑘𝑘−1; 𝑃𝑃𝑘𝑘|𝑘𝑘−1 = 𝐹𝐹𝑘𝑘−1,𝑃𝑃𝑘𝑘−1|𝑘𝑘−1𝐹𝐹𝑘𝑘−1

𝑇𝑇 + 𝑄𝑄𝑘𝑘−1; end

Step EKF update Data : 𝐱𝐱𝑘𝑘|𝑘𝑘−1,𝑃𝑃𝑘𝑘 |𝑘𝑘−1,𝐡𝐡𝑘𝑘(. ) Result : 𝐱𝐱𝑘𝑘|𝑘𝑘 ,𝑃𝑃𝑘𝑘 |𝑘𝑘

𝐻𝐻𝑘𝑘 = 𝜕𝜕𝐡𝐡𝑘𝑘𝜕𝜕𝐱𝐱𝐱𝐱𝑘𝑘|𝑘𝑘−1

;

𝑆𝑆𝑘𝑘 = 𝑅𝑅𝑘𝑘 + 𝐻𝐻𝑘𝑘𝑃𝑃𝑘𝑘 |𝑘𝑘−1𝐻𝐻𝑘𝑘𝑇𝑇 ; 𝐿𝐿𝑘𝑘 = 𝑃𝑃𝑘𝑘 |𝑘𝑘−1𝐻𝐻𝑘𝑘𝑇𝑇𝑆𝑆𝑘𝑘−1; 𝐞𝐞𝑘𝑘 = 𝐲𝐲𝑘𝑘 − 𝐡𝐡𝑘𝑘𝐱𝐱𝑘𝑘|𝑘𝑘−1; 𝐱𝐱𝑘𝑘|𝑘𝑘 = 𝐱𝐱𝑘𝑘|𝑘𝑘−1 + 𝐿𝐿𝑘𝑘𝐞𝐞𝑘𝑘 ; 𝑃𝑃𝑘𝑘|𝑘𝑘 = 𝑃𝑃𝑘𝑘 |𝑘𝑘−1 − 𝐿𝐿𝑘𝑘𝑆𝑆𝑘𝑘𝐿𝐿𝑘𝑘−1

𝑇𝑇 ; End

In OOA model, HA are specialized to describe mathematical behaviors, i.e. the dynamic model of quadrotor UAV including terms as Situations, Continuous State Variables, Event, Transition, Global Continuous Behavior and Invariants. A HA of the quadrotor UAV controller is defined in equation (6).

HQuadrotor UAV = (Q, X, ∑, A, Inv, F, qo, xo) (6) Where: - Q is a set of states describing flying modes of HQuadrotor UAV, e.g. the motion in horizontal translations, hovering, VTOL, rotations, roll, pitch, and yaw, which are combined with the local state machine oriented towards control modes (Fig. 3b) in permutations. Q can be called situations of the quadrotor UAV controller; qo is the initial situation. - X presents the continuous state space of HQuadrotor

UAV, X⊂ℜn, xco is the initial value of this space, e.g. continuous components of the quadrotor UAV

controller; xc∈X presents variables of which values are average in the occurred noises. - ∑ is a finite set of events, e.g. external interacting events from the guidance and navigation system, and environmental disturbances. - A is a set of transitions defined by (q, Guard, σ, Jump, q’) and represented by an arc between situations, here: q∈Q, q’∈Q; Guard is a subset of the state space in which the continuous state must be, so that the transition can be crossed; Jump represents the continuous state transformation during the change of situation; it is expressed by a state value function, whose result is affected like initial value of the continuous state in the new situation; σ∈∑ presents the event being associated in the transition; this association does not imply to give an input or output direction to the event. - Inv is an application, which associates a subset of the state space in each situation; it is called the

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invariant of the situation, in which the continuous state must remain, when the situation is q, the continuous state must verify xc∈Inv(q). - F is defined by using the six DoF dynamic model of quadrotor UAV, and the implemented functional block diagram (Fig. 4); the evolution of continuous state is occurred when the situation is activated. The constraints as follows: σ∈∑ is considered in

term of inputs/outputs and internality/externality; X contains input/output signals were applied to globally perform the HA evolution of a quadrotor UAV controller. In addition, the realization hypotheses of the HA evolution, which permit the invariant Inv and guard control Guard combined with transitions can generate internal events for the quadrotor UAV controller, are assumed in Table 1.

Table 1. Realization hypotheses of the HA evolution for a quadrotor UAV controller. Inv and Guard System evolution

If xq∉Inv(q) and Guard(a)=True, a∈A, then there is a generated internal event, and the system changes to the situation q’ described in a set of situations of the quadrotor UAV, with Jumpq’ identified by the initial value of the continuous fluid Fq’. This evolution is realized by the local state machines, e.g. the local state machine of the “Track a desired trajectory” use case (Fig. 3b).

If xq∈Inv(q) and Guard(a)=True, a∈A, then the system remains its actual situation q. If xq∈Inv(q) and Guard(a)=False, a∈A, then the system remains its actual situation q. If xq∉Inv(q) and Guard(a)=False, a∈A, then there is a generated internal event; the system changes into the

situation q”, which is called the irreversible default situation. 4.2 OOD model for a quadrotor UAV controller From the authors’ approach [52, 53], we have specialized the 5 main control capsules, which take part in the HA realization of the quadrotor UAV being developed: the continuous part’s capsule, discrete part’s capsule, internal interface’s capsule, external interface’s capsule and Instantaneous Global Continuous Behavior (IGCB’s capsule). Fig. 5 and Fig. 6 indicate respectively the real-time communication pattern, its structure and behaviors of main control capsules by using the real-time UML/MARTE’s collaboration and sequence diagrams. - The discrete part’s capsule contains a set of situations Q and transitions A in HA of the quadrotor UAV controller (i.e. the macro-motion in horizontal translations, hovering, VTOL, and rotations: roll, pitch, and yaw, which are combined with the local state machine (Fig. 3b) in permutations. - The continuous part’s capsule is combined with the continuous state space X in the implemented functional block diagram. The sequential evolution of continuous elements is carried out by specifying the Rendezvous pattern presented by [54] with two sub-capsules called RendezVous and Semaphore. - The IGCB’s capsule contains concrete global continuous behaviors of the quadrotor UAV being developed at time given just as f ∈ F in its HA. f is derived from (1), (5) and the implemented functional

block diagram (Fig. 4). This is also taken part into Algorithm 1 to estimate the position, depth, attitude and velocity of the quadrotor UAV. Each global continuous behavior corresponds to a situation in this HA.

Fig. 5. Real-time communication pattern for the main control capsules for a quadrotor UAV

controller. - The internal interface’s capsule verifies the Inv in HA of the quadrotor UAV controller, and generates internal events; so that the discrete part’s capsule can make its own evolution by these events. - The external interface’s capsule is an intermediary, which receives or sends episodic events and periodic signals between the developed quadrotor UAV and their interacted systems such as AES and MDS in our model. In Fig. 6, the messages exchanging between the main

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control capsules are synchronous, and the interval between two adjacent timeout messages indicates the sampling period (ΔT) of the IGCB’s capsule. The external interface’s capsule receives period signals coming from external continuous components. It then gives the ContinuousElement message to the IGCB’s capsule so that the IGCB’s capsule can call all of the continuous elements corresponding to the concrete ‘IGCB: IGCB1’. During the call of the IGCB’s capsule, the external interface’s capsule can receive an event named ‘3: InputEvent’ issued from the MDS or AES, and gives this event named ‘ee1: DetectedEvent’ to the discrete part’s capsule. The discrete part’s capsule then memorizes and later processes this event. If the IGCB’s capsule receives the LastContinuousElement message coming from

the continuous part’s capsule, then it gives the ContinuousEvolution message to the continuous part’s capsule so that the internal interface’s capsule can receive all updated variables. The internal interface’s capsule then verifies the invariant (Inv) of the situation q2; in this case, there is a generated internal event. The internal interface’s capsule gives this event to the discrete part’s capsule that permits the IGCB’s capsule to identify the concrete ‘IGCB: IGCB2’ and give output signals to the external interface’s capsule. At the end of this sampling period, the external interface’s capsule gives the output event and control signals to the external environment of the quadrotor UAV operating with its concrete ‘IGCB: IGCB2’.

Fig. 6. Sequential comunication messages in one sampling period (ΔT) of main control capsules for a quadrotor

UAV controller. Fig. 7 describes in detail the timing concurrency of evolutions for the above real-time communication pattern of main control capsules. Here, Ee1, Ee2, Ee3… are the external events coming from the external interface’s capsule; Ei1, Ei2, Ei3… are

internal events issued by the evolution of the internal interface’s capsule; q1, q2, q3… indicate the concrete situations in HA of the quadrotor UAV controller being developed; ec1, ec2, ec3… represent the evolutions of continuous elements in the

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continuous part’s capsule; and ∆T is a sampling period of the IGCB’s capsule. The realization hypotheses of timing concurrency for capsule evolutions in Fig. 7 are applied as follows: - If the end of the discrete part’s evolution is located before or just at the sampling date of the IGCB’s capsule, then the current IGCB model will change to the new IGCB model corresponding to this evolution; - If the end of the discrete part’s evolution is located after of appearing sampling date (∆T), then the current IGCB model is not commutated; - If an event appears during the evolution of the local state machine of UAV application (e.g. Fig. 3b), then this event is immediately memorized and solved later on; - All of the external and internal events have the same process by the discrete part’s capsule; - During the sampling period of the IGCB’s capsule, the continue part’s capsule, internal interface’s capsule and discrete part’s capsule make their own evolutions to possibly commutate to a new IGCB model, the IGCB continuous model remains in its current mode for this period;

Fig. 7. Timing concurrency of evolutions for main control capsules of a quadrotor UAV controller.

- So during the period of the IGCB’s capsule, the current IGCB model can detect two or more appeared situations (i.e. Q in HA), then the IGCB’s capsule synchronizes all these situations just at the end of this

period with the null timing duration; the current IGCB model subsequently changes to a new IGCB model, which corresponds to the last appeared situation during this period. In addition, the reusability is very important to implement controllers for different applications of UAVs typed VTOL because it permits the development time and cost to be reduced. The various reusable views in the development phase are considered as follows: The reusable view is based on the virtual mechanism of objects, classes or class hierarchies; the other re-use view can be based on design components, e.g. the implemented functional block diagram, the local state machine of quadrotor UAV controller and generic state machine of main control capsules that can be specified to develop various control applications of quadrotor UAVs using the same technique. The specializations, which permit the capsule collaboration of a developed quadrotor UAV to can be customizable and reusable in the new control application for various UAVs typed VTOL, can be seen in the author’s thesis [55]. 4.3 OOImpl models for a quadrotor UAV controllers To carry out the quadrotor UAV controller, the OOD model is firstly implemented to the OOImpl model (i.e. the simulation model) that is transformed from the above built OOD by using tools such as IBM Rational Rose RealTime or IBM Rational Software Architect RealTime [56] and Modelica/OpenModelica [15, 57]. Here, IBM Rational's leading role in defining the real-time UML is widely acknowledged, as is the pre-eminence of the IBM Rational Rose RealTime or IBM Rational Software Architect RealTime products in implementing UML to support the architecting of large-scale real-time and embedded software systems. It combines a rich modeling environment with a code-oriented tool set to create a comprehensive practitioner desktop for creating solutions in a variety of architectural styles, and targeted at specific runtime infrastructures. Many other important lifecycle artifacts also benefit from this tool (e.g. requirements lists, test cases and build scripts) to entirely cover development phases for the quadrotor UAV controller. Besides, OpenModelica is an open source modelling and simulation environment intended for industrial and academic usage. It is an object- oriented declarative multi-domain modelling language for complex dynamic systems. The OpenModelica environment allows most of the expression, algorithm, and function

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parts of Modelica to be executed interactively, as well as equation models and Modelica functions to be compiled into efficient C/C++ codes. The generated C/C++ codes are combined with a library of utility functions, a run-time library and a numerical Differential Algebraic Equation (DAE) solver. The obtained simulation results in OpenModelica permits us to theoretically evaluate the control performance and functionalities, and to easily optimize the control design elements before they are implemented and deployed. Then, the OOD model with the optimized control elements of simulation model is adapted to obtain the new updated OOD model for realization models of quadrotor UAV that will be called OOD* model. Finally, this OOD* model is converted into the new OOImpl* model (i.e. the realization model) by using

different specific platforms, which are based on the object-oriented Implementation Development Environment (IDE), e.g. the Arduino’s IDE [16] in order to completely realize the quadrotor UAV controller with compatible microcontrollers, e.g. ATMEGA32-U2 and STM32 Cortex-M4 microcontrollers [16]. A sketch of the above described model transformations is shown as Fig. 8. Here, the transformations are performed through the round-trip engineering (i.e. the forward and reverse engineering) of the intermediate C++ codes including about 80% of the generated codes and 20% of the hand-crafted codes, which are issued from the models depicted in IBM Rational Rose RealTime or IBM Rational Software Architect RealTime, OpenModelica tools and the Arduino’s IDE.

Fig. 8. Sketch of OOD-OOImpl model transformation for quadrotor UAV controllers. 5 Application Based on the above described model, a trajectory-tracking controller was developed that permits an autonomous quadrotor UAV reach and follow a geometric reference path in the Cartesian space starting from a given initial configuration. The main characteristics of this quadrotor UAV are resumed in Table 2. Table 2. Characteristics of the developed quadrotor

UAV. Parameter Value

Weight 4.50 kg Maximum payload 1.55 kg Autonomy 25 minutes Power Li-Po battery 22.2 V, 20000 mAh Maximum Take-off speed 7.5 m/s Maximum horizontal translation speed

8.5 m/s

Maximum altitude 500 m Maximum radius of action 4900 m

Inertia moment on x-axis Ixx 51.34e-3 kg.m2 Inertia moment on y-axis Iyy 51.34e-3 kg.m2 Inertia moment on z-axis Izz 11.18e-2 kg.m2 Rotor inertia of motor Jr 36.24e-5 kg.m2 Horizontal distance: propeller center to center of gravity l

0.515 m

All of artifacts of the analysis and design models have been created to entirely implement the trajectory-tracking controller of this quadrotor UAV that could be found in the author’s thesis [55]. We present here some of the control simulation results supposed as follows: the guidance system addresses a drive event of Taking-off to the quadrotor UAV with a desired altitude of 15 m; the transient control response in z-direction (z-Altitude) is shown as Fig. 9a; Fig. 9b brings out the transient control response in x-direction, when the quadrotor UAV received a drive event of Transferring with a desired distance of 15 m in x-direction (x-Position) from the current position. All of the obtained simulation results

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permit us to theoretically evaluate the control performance of this system within the control criteria such as the admissible timing response, transition and static errors. From that point, we can

decide to choose the designed control elements and their parametric values to perform the realization phase of this application.

Fig. 9. Transient control responses in z-direction (a) and in x-direction (b). The Arduino platform [16] was also used to quickly deploy the realization model for the controller. This platform can sense the environment by receiving input from a variety of sensors such as the pressure and magnetometer sensors, Inertial Measurement Unit (IMU), GPS, e.g. MPU6000 with working frequency 100Hz [58], Ublox Neo 6M with working frequency 10Hz [59], etc. and can affect its surroundings by controlled actuators. ATMEGA32-U2 and STM32 Cortex-M4 microcontrollers [16] have been used on the board, and can be programmed by using the Arduino programming language based on C++ and the object-oriented embedded programming C++. The trial flights were performed to test the

realization model of this application (Fig. 10a); the test scenarios were mainly based on the local state machine (Fig. 3b). We present here some of main test cases and obtained results for controlling the quadrotor UAV as follows: - 1st test scenario: the quadrotor UAV autonomously reaches and follows a desired rectangle-shaped trajectory with steer angles about 90o, the maximum trajectory error is about 1.8 m against each Way-Point (WP) position at these steer angles (Fig. 10b). - 2nd test scenario: the quadrotor UAV autonomously reaches and follows a desired quadrangular-shaped trajectory with steer angles about 120o, 30o and 150o, the maximum trajectory error is about 1.9 m against each WP position at these steer angles (Fig. 10c).

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- 3rd test case: the quadrotor UAV is autonomously capable of Vertical Take Off and Landing (VTOL) with a maximum altitude of 490 m; the landed

position error is 0.5 m against the initial taken off position.

(a)

(b)

(c)

Fig. 10. Setting up and testing the controller for the developed autonomous quadrotor UAV (a); Quadrotor UAV

reaches and follows a desired rectangle-shaped trajectory with steer angles about 90o (b); Quadrotor UAV reaches and follows a desired quadrangular-shaped trajectory with steer angles about 120o, 30o and 150o (c).

The trajectory-tracking controller of this autonomous quadrotor UAV was satisfied with performance requirements, e.g. the admissible control duration, transition and static errors that were based on the comparison between all of the experimental data corresponding with the obtained simulation results. The obtained results of control

performance were improved in comparison to the alone utilization of standard control methods such as the SMC, PID, LQ, IB or model predictive control. In this application, the standard control method of IB and the EKF algorithm were used for the altitude, position, and attitude control and the PID regulators were applied to the block of Motor Control that

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combined with HA and its evolution hypotheses of realization introduced in Table 1 to implement the functional block diagram (Fig. 4) for building up the ICCB’s capsule of OOD model. Within limit of the paper, we do not present here all the artefacts of the analysis, design and implementation model, and test results of the quadrotor UAV controller, so detailed results can be seen in the author’s thesis [55]. 6 Conclusions and future works This paper presented a model-based implementation to intensively realize controllers for quadrotor UAVs whose global behaviors can be considered as the HDS. This model is based on the specializations of MDA’s features combined with the real-time UML/MARTE, HA and EKF algorithm to closely analyze, design, implement and realize the control parts of system. No single formalism or language of an engineering process can possible capture all the knowledge and information needed to solve complex control systems such as the quadrotor UAV controller. The main points of this paper have been mentioned as follows:

• The quadrotor UAV dynamics and control structure are adapted for the control that are combined with the specialization of real-time object features including the OOA, OOD and OOImpl components.

• In the OOA model, the use case model is specialized with the implementable functional block diagram, EKF algorithm and HA together with its evolution hypotheses of realization (Table 1) to closely capture the requirements analysis for a quadrotor UAV controller.

• The OOD model is built for obtaining the detailed design model by specifying the real-time control capsules, ports, protocols enclosed with their timing concurrency of evolutions in order to model in detail the behaviors and structures of quadrotor UAV controllers. The developed OOD components are also used to create a real-time communication pattern that can be customized and reused in new UAV applications of which operating modes are capable of VTOL, hovering and horizontal flight.

• The OOD model with the optimized control elements is then adapted to obtain the new updated OOD model for the realization model. This updated OOD model is converted into new OOImpl models by using different object-oriented specific platforms in order to completely realize the quadrotor UAV controller with compatible

microcontrollers. • Based on this model, a trajectory-tracking

controller of a low-cost quadrotor was completely deployed and tested out Arduino ATMEGA U2 and STM32-Cortex-M4 microcontrollers. Up to now, we applied the above developed model just in the low-cost quadrotor UAV controller and intend to implement it in the new control applications for autonomous coordinated UAV. Eventually, if we get positive feedbacks, we will investigate in our application strategy to extend it more effective in order to completely make up controllers for balancing search and target response in cooperative team of various UAVs typed VTOL. Acknowledgements The authors would like to thank the material supports of the research project coded T2017-PC-058 at Hanoi University of Science and Technology, Vietnam. References: [1] N.P. Hung, N.V. Hien, P.G. Diem, N.P. Khanh,

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WSEAS TRANSACTIONS on SYSTEMS Hien N. V., Diem P. G.

E-ISSN: 2224-2678 61 Volume 18, 2019